(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(From Probability and Statistical Inference, Hogg and Tanis, Eighth Edition, 5.1-5)

The p.d.f. of X is [itex]f(x) = \theta x^{\theta - 1}[/itex] for [itex]0<x<1[/itex] and [itex]0<\theta<\infty[/itex]. Let [itex]Y = -2\theta \ln X[/itex]. How is [itex]Y[/itex] distributed?

2. Relevant equations

Um... Fundamental Theorem of Calculus?

3. The attempt at a solution

So I've actually solved this, it's exponential with [itex]\theta = 2[/itex]. My question is about the answer given in the back of the book: It cryptically says [itex]M(t) = (1-2t)^{-1}[/itex] for [itex]t<1/2[/itex] which is, to my eye, a useless calculation of the moment-generating function. WTF? Why is this here? Ideas?

Thank you.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Statistics - Distribution Function Technique

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